What are all the factors, the prime factorization, and factor pairs of 10?

Factors are the building blocks of numbers, the integers that multiply together to form a product. With the number 10 as our illustrative example, we embark on a journey to explore the intricate dance of multiplication that gives rise to 10. Understanding these factors illuminates the rich tapestry of mathematical relationships and properties inherent in the number 10.

Factors of 10 refer to the whole numbers which, when multiplied in pairs, yield the product 10. These factors are the essential elements that compose the number 10 in the multiplication process. Here is a list of the factors of 10:

• 1 x 10 = 10
• 2 x 5 = 10

Therefore, the factors of 10 are 1, 2, 5, and 10.

To determine the factors of 10, we can use the division method, which involves dividing 10 by smaller integers to see if the division results in a whole number without any remainder:

• 10 ÷ 1 = 10
• 10 ÷ 2 = 5
• 10 ÷ 5 = 2
• 10 ÷ 10 = 1

These resulting whole numbers are considered factors of 10. If the division does not result in a whole number, then the divisor is not a factor of 10. For instance, 10 ÷ 3 gives a quotient of 3.333, indicating that 3 is not a factor of 10.

Pair factors of a number consist of two numbers multiplied together to form that number. For the number 10, the pair factors are:

• (1, 10): 1 x 10 = 10
• (2, 5): 2 x 5 = 10

Negative numbers can also form pair factors, since the product of two negatives is positive:

• (-1, -10): -1 x -10 = 10
• (-2, -5): -2 x -5 = 10

The prime factorization of 10 involves breaking it down into its prime number components. This process reveals the most basic building blocks of 10. To find the prime factorization, we can create a factor tree:

• Start with 10 and determine the smallest prime number that divides it, which is 2.
• Next, determine the quotient of that division: 10 ÷ 2 = 5.
• Since 5 is a prime number, we have now found the prime factors of 10, which are 2 and 5.

The prime factorization of 10 can be written as 2 x 5.

As we delve into the factors of 10, here are some important points to keep in mind:

• The factors of 10 are 1, 2, 5, and 10.
• The prime factors of 10 are 2 and 5.
• The factor pairs of 10 are (1, 10) and (2, 5), and it also includes negative pairs (-1, -10) and (-2, -5).
• The sum of all the factors of 10 is 1+2+5+10 = 18.

These factors underline the properties of the number 10, presenting an insightful glimpse into its role within the realm of mathematics.

• Identify the pair factors of 10 that multiply to form a product greater than 10.
• List all the factors of 10 and calculate their product.

• Since 10 is a base-10 number, no pair factors can multiply to form a product greater than 10.
• The factors of 10 are 1, 2, 5, and 10. Their product is 1 x 2 x 5 x 10 = 100.